Alfvén wave amplification and self-containment of cosmic rays escaping from a supernova remnant

We study the escape of cosmic ray (CR) protons accelerated in a supernova remnant (SNR) by numerically solving a diffusion-convection equation for regions from the vicinity of the shock front to those far away from the front. We consider the amplifications of Alfvén waves generated by the escaping CR particles and their effects on CR escape into the interstellar medium (ISM). We find that the amplification of the waves significantly delays the escape of the particles even in regions far away from the shock front (on the scale of an SNR). This means that the energy spectrum of CR particles determined through γ-ray observations of molecular clouds around SNRs is seriously affected by the particle scattering by the waves.